Dimensional Formula

Dimensional Formula

IMPORTANT DIMENSIONAL FORMULAE

Dimensional Constants:
The physical quantities which have dimensions and have a fixed value are called as dimensional constants.
Ex: Gravitational Constant (G), Planck’s Constant (h), Universal gas constant (R), Velocity of light in vacuum (c) etc.,
Dimensional variables:
Dimensional variables are those physical quantities which have dimensions and do not have fixed value.
Ex:  Velocity, acceleration, force, work, power... etc
Dimensionless constants:
Dimensionless quantities are those which do not have dimensions but have a fixed value.
(a) Dimensionless quantities without units. 
 Ex: Pure numbers, pi(p) etc.,
(b) Dimensionless quantities with units.
 Ex: Angular displacement - radian, Joule’s constant-joule/calorie, etc.,
Dimensionless variables: 
Dimensionless variables are those physical quantities which do not have dimensions and do not have fixed value.
Ex: Specific gravity, refractive index, Coefficient of friction, Poisson’s Ratio etc.,
Advantages of Dimensions:
Advantages of describing a physical quantity in terms of its dimensions are as follows:
-    Describing dimensions help in understanding the relation between physical quantities and its dependence on base or fundamental quantities, that is how physical quantity rely on mass, time, length, temperature etc.
-    Dimensions are used in dimensional analysis, where we use them to convert from one system to another.
-    Dimensions are used in predicting unknown formulae by just studying how a certain physical quantity depends on base quantities and up to which extent.
-    It makes measurement and study of physical quantities easier.
-    We are able to identify or observe a quantity just because of its dimensions.
-    Dimensions define physical quantities & their existence.
Limitations of Dimensions:
-    Besides being a useful quantity, there are many limitations of dimensions, which are as follows:
-    Dimensions can’t be used for trigonometric and exponential functions.
-    Dimensions never define exact form of a relation.
-    We can’t find values of certain constants in physical relations with the help of dimensions.
-    A dimensionally correct equation may not be the correct equation always.